We present a novel protocol XORBoost for both training gradient boosted tree models and for using these models for inference in the multiparty computation (MPC) setting. Similarly to [AEV20], our protocol is the first one supporting training for generically split datasets (vertical and horizontal splitting, or combination of those) while keeping all the information about the features and thresholds associated with the nodes private, thus, having only the depths and the number of the binary trees as public parameters of the model. By using optimization techniques reducing the number of oblivious permutation evaluations as well as the quicksort and real number arithmetic algorithms from the recent Manticore MPC framework [CDG+21], we obtain a scalable implementation operating under information-theoretic security model in the honest-but-curious setting with a trusted dealer.
On a training dataset of 25,000 samples and 300 features in the 2-player setting, we are able to train 10 regression trees of depth 4 in less than 5 minutes per tree (using histograms of 128 bins).

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